Propagation Dynamics for a Spatially Periodic Integrodifference Competition Model

TL;DR

This paper investigates the propagation dynamics of a spatially periodic integrodifference competition model, revealing conditions under which a single spreading speed emerges, aligning with the minimal wave speed of traveling waves.

Contribution

It establishes that despite multiple potential speeds, the model admits a unique spreading speed under certain conditions, linking it to traveling wave theory.

Findings

The model admits a single spreading speed.

The spreading speed coincides with the minimal wave speed.

Sufficient conditions for linear determinacy are provided.

Abstract

In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means different species may have different spreading speeds. We show that the model system admits a single spreading speed, and it coincides with the minimal wave speed of the spatially periodic traveling waves. A set of sufficient conditions for linear determinacy of the spreading speed is also given.